Block #201,321

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 2:00:18 PM · Difficulty 9.8912 · 6,607,360 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

1ddbf50595fe47a382ea5418bc1deb7335e807d0ea2796506a482cbb4d68a074

View on Chainz ↗

Height

#201,321

Difficulty

9.891212

Transactions

Size

357 B

Version

Bits

09e42678

Nonce

9,178

Timestamp

10/9/2013, 2:00:18 PM

Confirmations

6,607,360

Mined by

⛏️ P2SHAbRjbCJACe6sD1GsBqx3xdMgNna5D3gsEs

Merkle Root

d6576a41fa7572e476ffa6733227f1bca808a6965e25f13bbcaf41676814eedb

Transactions (2)

Coinbase059ab4505ffdfd…6e1b830d43c544

1 in → 1 out10.2200 XPM109 B

AbRjbCJA…a5D3gsEs

6e512657067196…d732a0551609aa

1 in → 1 out10.2200 XPM159 B

Ae2P8tRG…ZBcRXaeZ

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.943 × 10⁹²(93-digit number)

69435472924647755944…72389325710996361599

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

6.943 × 10⁹²(93-digit number)

69435472924647755944…72389325710996361599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.943 × 10⁹²(93-digit number)

69435472924647755944…72389325710996361601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.388 × 10⁹³(94-digit number)

13887094584929551188…44778651421992723199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.388 × 10⁹³(94-digit number)

13887094584929551188…44778651421992723201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.777 × 10⁹³(94-digit number)

27774189169859102377…89557302843985446399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.777 × 10⁹³(94-digit number)

27774189169859102377…89557302843985446401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

5.554 × 10⁹³(94-digit number)

55548378339718204755…79114605687970892799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.554 × 10⁹³(94-digit number)

55548378339718204755…79114605687970892801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.110 × 10⁹⁴(95-digit number)

11109675667943640951…58229211375941785599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #201,321

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